Why is the commonly used Taylor series ln (1 + x) instead of LNX? It is the alpha power of (1 + x), not the alpha power of X

Why is the commonly used Taylor series ln (1 + x) instead of LNX? It is the alpha power of (1 + x), not the alpha power of X

To discuss the power series expansion of a function at a point, it is necessary to have the power series expansion at that point
The necessary condition is that the point is defined and differentiable of any order
Ln (x) is not defined at x = 0
If and only if α is a nonnegative integer, then the power series expansion is x ^ α itself
So we turn to the power series expansion at x = 1
After substitution, it is the power series expansion of Ln (1 + x) and (1 + x) ^ α at x = 0